Power from solar energy is not reliable, due to weather-related factors, which diminishes the power system’s reliability. Therefore, this study suggests a way to predict the intensity of solar irradiance using various statistical algorithms and artificial intelligence. In particular, we suggest the use of a hybrid predictive model, combining statistical properties and historical data training. In order to evaluate the maximum prediction steps of solar irradiance, the maximum Lyapunov exponent was applied. Then, we used the cosine similarity algorithm in the hidden Markov model for the initial prediction. The combination of the Hurst exponent and tail parameter revealed the self-similarity and long-range dependence of the fractional generalized Pareto motion, which enabled us to consider the iterative predictive model. The initial prediction was substituted into a stochastic differential equation to achieve the final prediction, which prevents error propagation. The effectiveness of the hybrid model was demonstrated in the case study.
Engineering applications of the fractional Weibull distribution (fWd) are quite limited because a corresponding stochastic process is not yet constituted and completely analyzed of fundamental properties. In order to fill this gap, the fractional Weibull process (fWp) is defined in this paper with the realization algorithm. The self-similarity property as well as long range dependence (LRD) are proven for the future research. The simulation is conducted by the actual data. The fWd is utilized to fit the actual probability distribution and the corresponding process is generated to reflect the stochasticity of the data. The random walk based on the fWp expands the simulation to the planar space.
In this paper, an adaptive remaining useful life prediction model is proposed for electric vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the multi-fractal Weibull motion. The varying degree of long-range dependence and the 1/f characteristics in the frequency domain are also analyzed. The age and state-dependent degradation model is derived, with the associated adaptive drift and diffusion coefficients. The adaptive mechanism considers the quantitative relations between the drift and diffusion coefficients. The unit-to-unit variability is considered a random variable. To facilitate the application, the convergence of the RUL prediction model is proved. Replacement of the lithium battery in the electric car is recommended according to the remaining useful life prediction results. The effectiveness of the proposed model is shown in the case study.
Currently, residual useful life (RUL) prediction models for insulated-gate bipolar transistors (IGBT) do not focus on the multi-modal characteristics caused by the pulse-width modulation (PWM). To fill this gap, the Markovian stochastic process is proposed to model the mode transition process, due to the memoryless properties of the grid operation. For the estimation of the mode transition probabilities, transfer learning is utilized between different control signals. With the continuous mode switching, fractional Weibull motion (fWm) of multiple modes is established to model the stochasticity of the multi-modal IGBT degradation. The drift and diffusion coefficients are adaptively updated in the proposed RUL prediction model. In the case study, two sets of the real thermal-accelerated IGBT aging data are used. Different degradation modes are extracted from the meta degradation data, and then fused to be a complex health indicator (CHI) via a multi-sensor fusion algorithm. The RUL prediction model based on the fWm of multiple modes can reach a maximum relative prediction error of 2.96% and a mean relative prediction error of 1.78%. The proposed RUL prediction model with better accuracy can reduce the losses of the power grid caused by the unexpected IGBT failures.
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